How do you delete a permanent bookmark on a Sprint Galaxy Tab 3?

Welcome to Android Central! Is this browser icon a shortcut you've placed on a homescreen, or are you tapping it in the App Drawer? Is it the stock Browser or Chrome?

Open the browser, tap Menu>Settings, and see if there is a way to change the homepage. If not, then that homepage might be hard-coded into the browser (you can thank Sprint for that). If it bothers you enough, use an alternative browser.